Aristotle Aristotle - Aristotle - The Complete Works

We conclude that in all our inquiries we are asking either whether there is a ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is precisely the cause, and it is the cause that we seek in all our inquiries. Thus, ‘Does the moon suffer eclipse?’ means ‘Is there or is there not a cause producing eclipse of the moon?’, and when we have learnt that there is, our next question is, ‘What, then, is this cause? for the cause through which a thing is-not is this or that, i.e. has this or that attribute, but without qualification is-and the cause through which it is-not is without qualification, but is this or that as having some essential attribute or some accident-are both alike the middle’. By that which is without qualification I mean the subject, e.g. moon or earth or sun or triangle; by that which a subject is (in the partial sense) I mean a property, e.g. eclipse, equality or inequality, interposition or non-interposition. For in all these examples it is clear that the nature of the thing and the reason of the fact are identical: the question ‘What is eclipse?’ and its answer ‘The privation of the moon’s light by the interposition of the earth’ are identical with the question ‘What is the reason of eclipse?’ or ‘Why does the moon suffer eclipse?’ and the reply ‘Because of the failure of light through the earth’s shutting it out’. Again, for ‘What is a concord? A commensurate numerical ratio of a high and a low note’, we may substitute ‘What ratio makes a high and a low note concordant? Their relation according to a commensurate numerical ratio.’ ‘Are the high and the low note concordant?’ is equivalent to ‘Is their ratio commensurate?’; and when we find that it is commensurate, we ask ‘What, then, is their ratio?’.

Cases in which the ‘middle’ is sensible show that the object of our inquiry is always the ‘middle’: we inquire, because we have not perceived it, whether there is or is not a ‘middle’ causing, e.g. an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth’s screening the sun’s light, and from this would arise the universal.

Thus, as we maintain, to know a thing’s nature is to know the reason why it is; and this is equally true of things in so far as they are said without qualification to he as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to right angles, or greater or less.

It is clear, then, that all questions are a search for a ‘middle’. Let us now state how essential nature is revealed and in what way it can be reduced to demonstration; what definition is, and what things are definable. And let us first discuss certain difficulties which these questions raise, beginning what we have to say with a point most intimately connected with our immediately preceding remarks, namely the doubt that might be felt as to whether or not it is possible to know the same thing in the same relation, both by definition and by demonstration. It might, I mean, be urged that definition is held to concern essential nature and is in every case universal and affirmative; whereas, on the other hand, some conclusions are negative and some are not universal; e.g. all in the second figure are negative, none in the third are universal. And again, not even all affirmative conclusions in the first figure are definable, e.g. ‘every triangle has its angles equal to two right angles’. An argument proving this difference between demonstration and definition is that to have scientific knowledge of the demonstrable is identical with possessing a demonstration of it: hence if demonstration of such conclusions as these is possible, there clearly cannot also be definition of them. If there could, one might know such a conclusion also in virtue of its definition without possessing the demonstration of it; for there is nothing to stop our having the one without the other.

Induction too will sufficiently convince us of this difference; for never yet by defining anything-essential attribute or accident-did we get knowledge of it. Again, if to define is to acquire knowledge of a substance, at any rate such attributes are not substances.

It is evident, then, that not everything demonstrable can be defined. What then? Can everything definable be demonstrated, or not? There is one of our previous arguments which covers this too. Of a single thing qua single there is a single scientific knowledge. Hence, since to know the demonstrable scientifically is to possess the demonstration of it, an impossible consequence will follow:-possession of its definition without its demonstration will give knowledge of the demonstrable.

Moreover, the basic premisses of demonstrations are definitions, and it has already been shown that these will be found indemonstrable; either the basic premisses will be demonstrable and will depend on prior premisses, and the regress will be endless; or the primary truths will be indemonstrable definitions.

But if the definable and the demonstrable are not wholly the same, may they yet be partially the same? Or is that impossible, because there can be no demonstration of the definable? There can be none, because definition is of the essential nature or being of something, and all demonstrations evidently posit and assume the essential nature-mathematical demonstrations, for example, the nature of unity and the odd, and all the other sciences likewise. Moreover, every demonstration proves a predicate of a subject as attaching or as not attaching to it, but in definition one thing is not predicated of another; we do not, e.g. predicate animal of biped nor biped of animal, nor yet figure of plane-plane not being figure nor figure plane. Again, to prove essential nature is not the same as to prove the fact of a connexion. Now definition reveals essential nature, demonstration reveals that a given attribute attaches or does not attach to a given subject; but different things require different demonstrations-unless the one demonstration is related to the other as part to whole. I add this because if all triangles have been proved to possess angles equal to two right angles, then this attribute has been proved to attach to isosceles; for isosceles is a part of which all triangles constitute the whole. But in the case before us the fact and the essential nature are not so related to one another, since the one is not a part of the other.

So it emerges that not all the definable is demonstrable nor all the demonstrable definable; and we may draw the general conclusion that there is no identical object of which it is possible to possess both a definition and a demonstration. It follows obviously that definition and demonstration are neither identical nor contained either within the other: if they were, their objects would be related either as identical or as whole and part.

So much, then, for the first stage of our problem. The next step is to raise the question whether syllogism-i.e. demonstration-of the definable nature is possible or, as our recent argument assumed, impossible.

We might argue it impossible on the following grounds:-(a) syllogism proves an attribute of a subject through the middle term; on the other hand (b) its definable nature is both ‘peculiar’ to a subject and predicated of it as belonging to its essence. But in that case (1) the subject, its definition, and the middle term connecting them must be reciprocally predicable of one another; for if A is to C, obviously A is ‘peculiar’ to B and B to C-in fact all three terms are ‘peculiar’ to one another: and further (2) if A inheres in the essence of all B and B is predicated universally of all C as belonging to C’s essence, A also must be predicated of C as belonging to its essence.